Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
typedef long long i64;
using std::cout;
using std::endl;
using std::cin;

int main() {
	int n; cin >> n; std::vector<int> a(n);
	for(int i = 0; i < n; i++) cin >> a[i];
	sort(begin(a), end(a));
	
	double ma = 0;
	for(int i = 0; i < n - 1; i++) {
		double tmp = 0;
		for(int j = n - 1, c = 0; j >= 0 and c < 2; j--) {
			if(j == i || j == i + 1) continue;
			tmp += a[j]; c++;
		}
		
		ma = std::max(ma, tmp / (a[i + 1] - a[i]));	
	}
	
	cout << std::fixed << std::setprecision(10) << ma << endl;
	return 0;
}